Ground state of a Bose-Einstein condensate which scatters coherently laser radiation

We present a self-consistent method of taking into account back action of a laser radiation to a Bose-Einstein condensate of neutral atoms. The light is coherently scattered inside the degenerate atomic sample, thus its intensity and, consequently, the atomic ground level AC Stark shift are spatially varying. This leads to a small deformation of the atomic cloud and, if the external radiation is abruptly switched off, to generation of collective excitations. Received 8 May 1999 and Received in final form 11 October 1999